Galactic rotation and solar motion from stellar kinematics

I present three methods to determine the distance to the Galactic Centre R₀, the solar azimuthal velocity in the Galactic rest frame V_{g, ⊙} and hence the local circular speed V_c at R₀. These simple, model-independent strategies reduce the set of assumptions to near-axisymmetry of the disc and are designed for kinematically hot stars, which are less affected by spiral arms and other effects. The first two methods use the position-dependent rotational streaming in the heliocentric radial velocities (U). The resulting rotation estimate θ from U velocities does not depend on V_{g, ⊙}.

The first approach compares this with rotation from the Galactic azimuthal velocities to constrain V_{g, ⊙} at an assumed R₀. Both V_{g, ⊙} and R₀ can be determined using the proper motion of Sgr A* as a second constraint. The second strategy makes use of θ being roughly proportional to R₀. Therefore a wrong R₀ can be detected by an unphysical trend of V_{g, ⊙} with the intrinsic rotation of different populations. From these two strategies I estimate R₀ = (8.27 ± 0.29) kpc and V_{g, ⊙} = (250 ± 9) km s^-1 for a stellar sample from Sloan Extension for Galactic Understanding and Exploration, or, respectively, V_c = (238 ± 9) km s^-1. The result is consistent with the third estimator, where I use the angle of the mean motion of stars, which should follow the geometry of the Galactic disc. This method also gives the solar radial motion with high accuracy.

The rotation effect on U velocities must not be neglected when measuring the solar radial velocity U_⊙. It biases U_⊙ in any extended sample that is lop-sided in position angle α by of the order of 10 km s^-1. Combining different methods I find U_⊙ ∼ 14 km s^-1, moderately higher than previous results from the Geneva-Copenhagen Survey.